PCB-Based Current Sensor Design for Sensing Switch Current of a Nonmodular Gan Power Semiconductor

energies

Article PCB-Based Current Sensor Design for Sensing Switch Current of a Nonmodular GaN Power Semiconductor

Ui-Jin Kim , Min-Soo Song and Rae-Young Kim * The Department of Electrical and Biomedical Engineering, Hanyang University, Seoul 04763, Korea; [email protected] (U.-J.K.); [email protected] (M.-S.S.) * Correspondence: [email protected]; Tel.: +82-2-2220-2897

Received: 27 August 2020; Accepted: 30 September 2020; Published: 3 October 2020

Abstract: GaN-based power semiconductors exhibit small on-resistance and high dv/dt of the switch characteristics, thereby enabling the construction of high-efficiency, high-density semiconductor systems with fast switching and low power loss characteristics and miniaturization of passive devices. However, owing to the characteristics of GaN devices that result in them being significantly faster than other devices, the accuracy of the switching transient response significantly affects the noise or inductance in the device. Therefore, securing sufficient sensor bandwidth is considerably important for accurate current measurement in GaN-based devices. Conversely, the current sensor in the form of a non-insulated coil must secure sufficient bandwidth and overcome the tradeoff relationship with measurement sensitivity; moreover, the sensor configuration must be applicable to various power semiconductor types. This study proposes a current sensor model that applies the principle of the printed circuit board Rogowski coil to a surface mount device-type GaN-based half-bridge structure. This structure is applicable to a nonmodular power converter and is designed to secure sufficient bandwidth with a minimum area while simultaneously exhibiting high sensitivity. For the coil design, mutual inductances with existing coil structures were compared and analyzed, and the frequency response and magnetic analysis were evaluated. Experimental verification was performed and the transient response characteristics in various DC voltage ranges are discussed.

Keywords: gallium nitride (GaN); current sensor; Rogowski coil; pick-up coil; double pulse test; bandwidth; sensitivity

1. Introduction In recent times, power semiconductors, such as SiC and GaN, having wide band gap characteristics have contributed significantly to improving the efficiency and density of power converters owing to their low power consumption, miniaturization of passive devices, and high stability at high temperatures [1,2]. Among them, GaN devices have the advantage of having a faster switching speed than conventional Si device-based power semiconductors owing to their low on-resistance and device inductance [2–5]. However, vulnerability to external noise due to high dv/dt of the switch and peak current generation in overcurrent situations can cause problems in stable system operation [6]. Therefore, the analysis of switching current information, which is an important variable for current control, system diagnosis, and protection, is significantly important for evaluating the device model and its characterization. Consequently, an accurate current sensor with sufficient bandwidth (>1 MHz) is required [7]. Current sensor technologies that can be used in various bandwidth, insulation, and measurement conditions predominantly include methods using Ohm’s law of resistance [8–10], magnetic field sensors [11–15], and Faraday’s induction law [16–25]. The shunt resistor is a representative sensor that uses the principle of Ohm’s law of resistance. This method measures the current through a voltage

Energies 2020, 13, 5161; doi:10.3390/en13195161 www.mdpi.com/journal/energies Energies 2020, 13, 5161 2 of 15 drop phenomenon applied to a resistor composed of a material having a low temperature coefficient of resistance. The relatively low price and rapid and accurate responses are the advantages of shunt resistors; however, the proximity and skin effects of the conductor line can lower the measurement accuracy due to the variable frequency. In addition, the relatively large size and characteristics of having a large parasitic inductance value of several nanohenries are other limitations when analyzing power semiconductors such as GaN that require rapid switching operation [8]. Hall-effect sensors and magnetoresistors are current sensors that generate static and dynamic magnetic flux through magnetic field sensors; they are common technologies used for isolated current sensing with the capability of DC and AC measurement. In the case of double Hall-effect sensors, significant technological improvement has been achieved in recent years; however, there are problems of limited bandwidth range and lower measurement accuracy corresponding to a relative frequency range [15]. A magnetic resistor composed of a semiconductor and several metal alloys is a magnetic field detector that responds to the horizontal component of a magnetic field and typically includes open-loop technology [15], closed-loop technology [15], and hybrid-type sensor technology with other current sensors [11,13,14]. Methods using the Faraday’s law typically include current transformers (CTs) and the Rogowski coils. The CT is a galvanic insulation sensor that uses a coil, which is a core material with high magnetic permeability, to estimate the original current by measuring the magnetic flux generated by the primary current to be measured through the induction principle of Faraday [14,18]. The CT is a widely researched and commercialized sensor method; however, owing to the characteristics of the ferromagnetic core constituting the coil, it has a nonlinear characteristic that is saturated in a high-frequency and overcurrent-type environment and demonstrates the disadvantages of large core loss and limited current measurement range [15]. The Rogowski coil includes a sensor that measures the AC when the magnetic flux generated by the primary current flows inside the toroidal air core, as in the case of the CT. At this time, the coil composed of the air core is unsaturated regardless of the current range and has the advantage of lower core loss and wideband current measurement. However, the use of the air core demonstrates a problem of low sensitivity and requires a process of restoring voltage information to current information using a series of integrators [19–24]. Conversely, in the case of the conventional toroidal Rogowski coils, the position between the sensor coil and the conductor to be measured has a significant influence on the measurement accuracy. Moreover, in recent years, a printed circuit board (PCB)-based Rogowski coil has been proposed to increase the accuracy of the position [25–28]. In addition, various studies were conducted on coil design for higher sensitivity improvement. However, there is a limitation in that a separate external PCB layer is required to construct a toroidal Rogowski coil that wraps the conductor through which the primary current flows, and it cannot be applied to nonmodular power converters when measuring the switch current [20] and [25]. To overcome this spatial limitation, a pick-up coil capable of constructing a PCB with a current measurement method using the same principle as that of the Rogowski coil was proposed [29] and [30]. The pick-up coil is configured in a limited area, rather than surrounding the conductor in all directions; consequently, a part of the induced magnetic flux generated by the primary current is picked up and transferred into the coil. Therefore, it does not require a separate additional external PCB for the sensor coil and is applicable to nonmodular power converters. However, when compared to the existing Rogowski coil of toroidal-form windings, there are problems of sensitivity due to reduced inductance and technical limitations of using the through-hole technology in PCB construction [4,31]. In addition, in the case of next-generation semiconductors such as GaN power semiconductors, it is necessary to secure sufficient sensor bandwidth to measure the switch current in the transient state. This study proposes a coil structure that can increase the sensor sensitivity by maximizing the amount of induced magnetic flux through a double-layer rectangular shape coil in a limited space while achieving a high sensor sensitivity. The remainder of this paper is organized as follows. Section2 presents the basics of conventional pick-up coils embedded in PCB circuits. The basic operating principle and parameter analysis according Energies 2020, 13, x FOR PEER REVIEW 3 of 16

The remainder of this paper is organized as follows. Section 2 presents the basics of conventional Energies 2020, 13, 5161 3 of 15 pick-up coils embedded in PCB circuits. The basic operating principle and parameter analysis according to the coil shape were performed and presented. The design of the proposed coil model is toexplained the coil shape in Section were performed3, considering and presented.different types The designof coils of and the integrators. proposed coil Section model 4 ispresents explained the inexperimental Section3, considering verification di offferent this study types and of coils the andconclusion integrators. is presented Section 4in presents Section 5. the experimental verification of this study and the conclusion is presented in Section5. 2. Analysis of Current Sensor Coil 2. Analysis of Current Sensor Coil 2.1. Current Sensor Using Faraday’s Law Principle 2.1. Current Sensor Using Faraday’s Law Principle Figure 1 illustrates the principle of a current sensor using a pick-up coil to which the principle Figure1 illustrates the principle of a current sensor using a pick-up coil to which the principle of of Faraday’s law is applied. The pick-up coil is comprised of a trace pattern of the air core and certain Faraday’s law is applied. The pick-up coil is comprised of a trace pattern of the air core and certain vias. The magnetic flux generated by the primary current i1 flowing in the trace enters the pick-up i vias.coil and The generates magnetic fluxan electromotive generated by force the primary(EMF) at current the coil 1terminal.flowing The in the EMF trace is a enters value the obtained pick-up by coilmultiplying and generates the rate an of electromotive time change forceof the (EMF) primary at the current coil terminal.and the mutual The EMF inductance is a value between obtained the bysensor multiplying coil and the therate conductor, of time as change presented of the below primary [25]. current and the mutual inductance between the sensor coil and the conductor, as presented below [25].

i1 Lc Rc

vcoil

e Cc vcoil S

(a) (b)

FigureFigure 1. SchematicSchematic diagram diagram of a of pick-up a pick-up coil: coil:(a) principle (a) principle of a pick-up of a pick-up coil; (b) coil;equivalent (b) equivalent lumped lumpedcircuit. circuit.

dφ di di ()=−dφ =−μ ⋅ ⋅11di =−1 di1 e(ett) = N= oµo NSN S = M M (1)(1) − dt − · · dtdt − dt dt Further,Further, the the mutual mutual inductance inductance is obtainedis obtained as definedas defined in Equationin Equation (2). (2). Here, Here,µo is µ permeabilityo is permeability of 7 freeof free space, space, which which equals equals 4π 4π10 ×− 10H−7 /H/m,m, N Nis is the the turn turn number number of of the the coil, coil, and andS Sis is the the inner inner area area of of × thethe core core through through which which the magneticthe magnetic flux passes.flux passes. The mutual The mutual inductance inductance is proportional is proportional to the number to the ofnumber turns, and of turns, the measurement and the measurement sensitivity se isnsitivity determined is determined accordingly. accordingly. M =⋅⋅μ NS o (2) M = µo N S (2) · · Moreover, when the primary current i1 flows into the coil circuit, the coil can be equalized using a lumpedMoreover, model, when as illustrated the primary in current Figure i1b,1 flows where into the the coil-induced coil circuit, voltage the coil is can expressed be equalized as follows: using a lumped model, as illustrated in Figure1b, where the coil-induced voltage is expressed as follows: di 1 t et()=++⋅ L Ri i dt (3) cc0 Z t dtdi Cc 1 e(t) = Lc + Rci + i dt (3) where Lc is the magnetization inductance ofdt the coil, RcC isc the0 self-resistance· value of the coil, Cc is the self-capacitance value of the coil. where L is the magnetization inductance of the coil, R is the self-resistance value of the coil, C is c c c the self-capacitance value of the coil.

Energies 2020, 13, 5161 4 of 15 Energies 2020, 13, x FOR PEER REVIEW 4 of 16 Energies 2020, 13, x FOR PEER REVIEW 4 of 16 2.2. Pickup Coil Model Built in PCB 2.2.2.2. Pickup Pickup Coil Coil Model Model Built Built in in PCB PCB In the PCB model of the existing pick-up coil [30], the sensor coil is a vertical structure on the InIn the the PCB PCB model model of of the the existing existing pick-up pick-up coil coil [30], [30 the], the sensor sensor coil coil is a isvertical a vertical structure structure on the on conductor trace where the current flows; moreover, the sensor coil is composed of trace lines and vias, conductorthe conductor trace tracewhere where the current the current flows; flows;moreover, moreover, the sensor the coil sensor is composed coil is composed of trace lines of trace and vias, lines and is configured to transfer the magnetic flux generated by the primary current inside the coil in andand is vias, configured and is configured to transfer tothe transfer magnetic the flux magnetic generated flux by generated the primary by the current primary inside current the coil inside in Figure 2. Figurethe coil 2. in Figure2.

` Coil ɸ Coil ɸ

i1 i1

Figure 2. Conventional printed circuit board (PCB) pick-up coil design. FigureFigure 2. 2. ConventionalConventional printed printed circuit circuit bo boardard (PCB) (PCB) pick-up pick-up coil coil design. design. Figure 3 shows the vector distribution of the magnetic flux density between the sensor and the FigureFigure 3 showsshows the the vector vector distribution distribution of the of themagnetic magnetic flux density flux density between between the sensor the and sensor the conductor when a conductor current of 5A flows through a conventional pick-up coil. In this case, conductorand the conductor when a conductor when a conductorcurrent of 5A current flows of th 5Arough flows a conventional through aconventional pick-up coil. pick-upIn this case, coil. when the current flows through vias, the number of vias increases as the turn numbers of the coil whenIn this the case, current when flows the current through flows vias, through the number vias, the of numbervias increases of vias as increases the turn as numbers the turn numbersof the coil of increases, which can result in PCB overheating and an increase in loop impedance owing to uneven increases,the coil increases, which can which result can in resultPCB overheating in PCB overheating and an increase and an increasein loop impedance in loop impedance owing to owing uneven to distribution and the bottleneck of the current flowing on the PCB [31]. Thus, as the number of turns distributionuneven distribution and the bottleneck and the bottleneck of the current of the currentflowing flowing on the PCB on the [31]. PCB Thus, [31]. as Thus, the number as the number of turns of of the coil increases, the self-inductance and sensitivity of the coil increases. ofturns the coil of the increases, coil increases, the self-inductance the self-inductance and sensitivity and sensitivity of the ofcoil the increases. coil increases.

(a) (b) (a) (b) Figure 3. PCBPCB circuit analys analysisis using finite finite element method: ( a)) side side view; view; ( (b)) top view. Figure 3. PCB circuit analysis using finite element method: (a) side view; (b) top view. In this study, thethe groupsgroups of pick-uppick-up coils according to their shap shapeses include fishbone, fishbone, saw blade, In this study, the groups of pick-up coils according to their shapes include fishbone, saw blade, triangle-shaped, andand rectangle-shaped rectangle-shaped types. types. The Th numbere number of turns of turns and shape and shape of the coilsof the were coils adjusted were triangle-shaped, and rectangle-shaped types. The number of turns and shape of the coils were duringadjusted the during design the stage design such stage that the such same that mutual the sa inductanceme mutual value inductance is achieved value between is achieved the conductor between adjusted during the design stage such that the same mutual inductance value is achieved between throughthe conductor which thethrough primary which current the flowsprimary and current the coil. fl Theows valuesand the of thecoil. di Thefferent values parameters of the aredifferent listed the conductor through which the primary current flows and the coil. The values of the different inparameters Table1. Moreover, are listed thein Table PCB configuration 1. Moreover, accordingthe PCB configuration to the shape ofaccording the coil andto the inductance shape of the values coil parameters are listed in Table 1. Moreover, the PCB configuration according to the shape of the coil obtainedand inductance by the values finite element obtained method by the werefinite compared element method and analyzed. were compared and analyzed. and inductance values obtained by the finite element method were compared and analyzed.

Energies 2020, 13, x FOR PEER REVIEW 5 of 16

Table 1. Comparison of the dependent coil structure.

Pattern EnergiesEnergiesEnergies Energies20 20,20 2013, 20 ,120 x3, , 20FOR 1x3 ,FOR, 1x3 PEERFOR, x PEER FOR PEER REVIEW PEERREVIEW REVIEW REVIEW Fishbone Saw Blade Triangle Rectangle 5 of5 of165 16 of5 16of 16 EnergiesEnergiesEnergies Energies20 2020,20 2013, 20,201 x3, 20, FOR 1x3, Structure FOR,1 x3 PEER,FOR x PEERFOR PEER REVIEW PEER REVIEW REVIEW REVIEW 5 of5 16of5 16of5 16of 16 Energies 2020, 13, 5161 5 of 15 TableTableTable 1.Table 1.Comparison Comparison1. Comparison1. Comparison of ofthe theof dependent theof dependent the dependent dependent coil coil structure coil structure coil structure structure. . . . TableTableTable 1.Table Comparison1. Comparison1. Comparison1. Comparison of ofthe theof dependent ofthe dependent the dependent dependent coil coil structure coil structure coil structure structure. . . . SkeletonPatternPatternPatternPattern PatternPatternPatternPattern Table 1. FComparisonishboneFishboneFishboneFishbone ofS theawS aw dependent SBladeaw SBladeaw Blade Blade coilT riangleT riangle structure.TriangleTriangle Rectangle RectangleRectangleRectangle StructureStructureStructureStructure i1 i i i FishboneFishboneFishboneFishbone S awS aw SBladeaw S1Bladeaw Blade Blade T riangleT riangleT1 riangleTriangle Rectangle RectangleRectangle1Rectangle StructureStructureStructure Pattern StructureStructure Fishbone Saw Blade Triangle Rectangle SkeSkeletonSkeletonSkeleton leton SkeSkeletonSkeletonSkeleton leton SkeletonPCB Layout i1 i1 i1 i1 i1 i1 i1 i1 i1 i1 i1 i1 i 1 i1 i1 i1 i1 i1 i1 i i i i i i i 1 i1 1 1 i1 i1 1 1 i1 i1 1 1 i1

Mutual PCB LayoutPCBPCBPCB Layout PCBLayout Layout Layout 1.15 nH 1.15 nH 1.15 nH 1.15 nH InductancePCBPCBPCB LayoutPCB Layout Layout (LayoutM ) Self 20.14 nH 19.23 nH 19.14 nH 12.65 nH Inductance (Ls) Mutual InductanceMutualMutualMutual (MMutual ) 1.15 nH 1.15 nH 1.15 nH 1.15 nH Self InductanceLs/M (L ) 20.141.151.1517.5 1.15nH nH nH 1.15 nH nH 1.1 19.231.116.75 1.1nH5 nH 1.1 nH5 nH5 nH 1.15 1.1516.6 19.141.15nH nH 1.15 nH nH nH 1.151.15 11 1.15nH 12.65nH1.15 nH nH InductanceInductanceMutualInductanceMutualInductanceMutualsMutual (M (M) ()M ()M ) Ls/M 1.151.1517.5 1.15nH 1.15nH nH nH 1.1 1.15 16.71.1nH5 1.1nH5 nH5 nH 1.15 1.15 1.15nH 1.15nH 16.6 nH nH 1.151.15 1.15nH 1.15nH nH 11 nH InductanceInductanceInductanceSelfInductanceSelf Self (SelfM ( M) ( )M (M) ) Current sensorsSelfSelf used Self Self in GaN20.14 20.14devices20.14 nH20.14 nH nHare nH required19.23 19.2319.23 nH19.23 nH to nH simultaneously nH 19.1419.14 19.14 nH19.14 nH nH nH secure12.65 12.6512.65 nHhigh12.65 nH nH sensitivity nH and InductanceInductanceInductanceInductance (L (sL) s()L s()20.14L s20.14) 20.14 nH20.14 nH nH nH 19.23 19.2319.23 nH19.23 nH nH nH19.14 19.1419.14 nH19.14 nH nH nH 12.65 12.6512.65 nH12.65 nH nH nH bandwidth.Current sensorsBecauseInductanceInductance used the bandwidth in (sL GaN s()L s) s devices (BW) of are the required coil is significantly to simultaneously influenced secure by the high self-inductance sensitivity InductanceLInductancesL/Ms/LM s /(L MLs/) M (L )17.5 17.5 17.5 17.5 16.716.7 16.7 16.7 16.616.6 16.6 16.6 1111 11 11 value of the coil as seen (4), the coil must have a minimum self-inductance value Lc to ensure sufficient and bandwidth. BecauseLs/LMs/ theLM s/L M bandwidths/M 17.517.5 (BW) 17.5 17.5 of the coil16.716.7 is 16.7 significantly 16.7 16.616.6 influenced16.6 16.6 by1111 the 11 self-inductance11 bandwidth. Further, the coil must have high sensor sensitivity because it is configured to allow value ofCurrentCurrent theCurrent coilCurrent sensors assensors seensensors sensors used (4), used used thein usedin GaN coil inGaN in mustGaN devices GaNdevices devices have devices are aare minimumrequired are required are required required to self-inductance to simultaneously stoimultaneously tosimultaneously simultaneously value secure secure Lsecurec tosecurehigh high ensure high sensitivity highsensitivity susensitivity ffisensitivitycient and and and and maximum magnetic flux inside the core. 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Therefore, the when the whenwidest the widestwhen the designing whenwidest designing widestbandwidth designing bandwidth designing bandwidth bandwidtha sensora sensor acan sensoracan sensor can can coilbebecoil selected based coilbeselected basedcoilbe selected based selected onbased. on. a on .specifica onspecific . a specifica specific sensitivity, sensitivity, sensitivity, sensitivity, a rectangulara rectangulara rectangulara rectangular coil coil modelcoil modelcoil model modelrepresenting representing representing representing the the widest the widest the widest widest bandwidth bandwidth bandwidth bandwidth can can can can bebe selected beselectedbe selected selected. . . .

(a) (b)

FigureFigure 4. 4.Comparison Comparison between between pick-up pick-up coils coils without without integrator: integrator: (a )(a frequency) frequency response response of of sensor sensor coil coil

at atM M= 1.15= 1.15 nH; nH; (b ()b coil) coil sensitivity sensitivity at atLs L=s =19 19 nH. nH.

(a)( a)( a)( a) (b()b )( b)( b) 1 (a)( a)( a)(BW a) = f f f = 1 (b()b )( b()b ) (4) BW=−≈=res f fc f res FigureFigureFigure 4.Figure 4.Comparison Comparison4. Comparison4. Comparison between between between between pick pick- pickup- uppick coilsres- upcoils−-up coilswithout c ≈withoutcoils without res without integrator: integrator: 2integrator:π integrator:√L c(aC )(c afrequency) (farequency) ( farequency) frequency response response response response of ofsensor sensorof sensorof coil sensor coil coil (4) coil FigureFigure 4. Comparison4. Comparison between between pick pick-up-up coils coils without without2 integrator:π integrator:LC (a) (farequency) frequency response response of sensorof sensor coil coil Figureat atM Mat= 1.154.Figure=Mat 1.15Comparison M= nH;1.15 = nH; 4.1.15 ( nH;bComparison )( bnH;c) oil( cb betweenoil )(sensitivity bc oil)sensitivity c oilsensitivity between sensitivitypick at- upatLs pickL= atcoilss 19 =Lat s-19 nH.up= Lwithout s19nH. =coils 19nH. nH. without integrator: integrator:cc (a) frequency (a) frequency response response of sensor of coilsensor coil where fres is the resonant frequency of sensor and fc is the cutoﬀ frequency of sensor. at atM Mat= 1.15 at=M 1.15 M= nH;1.15 = nH;1.15 ( nH;b )( nH;bc )oil( bc oil )(sensitivity bc )oilsensitivity coil sensitivity sensitivity at atLs L=at s19 =atL s 19 nH.L= s19 nH.= 19nH. nH. where fres is the resonant frequency of sensor and fc is the cutoff frequency of sensor. 3. Design of the Proposed Pick-Up Coil 1 1 1 1 BWBW=BW= fBW f= −≈ f= f−≈ f −≈ f f −≈ f f = f = f = = resresres c cres res c res c resπ res1 1 1 1 (4)(4) (4) (4) BWBW=BW= fBW f= −≈= f −≈ f −≈ f f−≈ f f = f2 = f2 =πLC2 =ccπLC2ccπLC ccLC cc resresres cres c res c res c res resπ π (4)(4) (4) (4) 3.1. Basic Structure of the Rectangular Pick-Up Coil 2π2 LC2ccLC2ccπLCccLCcc wherewherewhere wherefres f resis fistheres ftheisres resonant theis resonant the resonant resonant frequency frequency frequency frequency of of sensor ofsensor ofsensor sensorand and fandc is fandc is thefc theis f ccutoff theis cutoff the cutoff frequencycutoff frequency frequency frequency of of sensor ofsensor ofsensor .sensor . . . wherewhereres fres fisres theresis the resonant resonant frequency frequency of ofsensor sensor and andc fc is fc theisc the cutoff cutoff frequency frequency of ofsensor sensor. . where The wheref proposed is the f resonant is coilthe resonant is frequency in the frequency form of of sensor two of sensorturnsand f of isand the f cutoff rectangularis the frequencycutoff shapefrequency of onsensor a of two-layer .sensor . design; moreover, the trace through which the primary current ﬂows wraps the sensor coil on three sides.

EnergiesEnergies 2020 20, 1203, x13 FOR, x FOR PEER PEER REVIEW REVIEW 6 of6 of16 16

3. Design3. Design of theof the Proposed Proposed Pick Pick-Up-Up Coil Coil

3.1.3.1. Basic Basic Structure Structure of theof the Rectangular Rectangular Pick Pick-Up-Up Coil Coil The proposed coil is in the form of two turns of the rectangular shape on a two-layer design; EnergiesThe2020 proposed, 13, 5161 coil is in the form of two turns of the rectangular shape on a two-layer design;6 of 15 moreover,moreover, the the trace trace through through which which the the primary primary current current flowsflows wraps the sensorsensor coil coil on on three three sides. sides. The width of the coil trace is 0.4 mm, and the spacing between the coil and the trace through which The width of the coil trace is 0.4 mm, and the spacing between the coil and the trace through which Thethe width primary of thecurrent coil traceon the is three 0.4 mm, sides and flows the is spacing 0.17 mm between as shown the in coilFigure and 5a. the trace through which the primary current on the three sides flows is 0.17 mm as shown in Figure 5a. the primary current on the three sides ﬂows is 0.17 mm as shown in Figure5a.

ɸ1+ɸ2+ɸ3 ɸ1+ɸ2+ɸ3 (top layer) (top layer) out out ɸ1 ɸ1 (middle layer) (middle layer) I1

I1 ɸ3 ɸ3 (bottom layer) ɸ2 (bottom layer) id ɸ2

id (a) (b) Figure 5. Proposed(a) sensor coil structure: (a) description of the proposed( bcoil;) (b) PCB layout.

FigureFigure 5. 5. ProposedProposed sensor sensor coil coil structure: structure: (a ()a )description description of of the the proposed proposed coil; coil; (b (b) )PCB PCB layout. layout. Accordingly, the magnetic flux component on the three sides due to the primary current flowing in the plane of the bottom layer flows into the coil in the same direction and maximizes the mutual Accordingly,Accordingly, the the magnetic magnetic flux flux component component on on the the three three sides sides due due to to the the primary primary current current flowing flowing ininductance the plane of value the bottomof the pick layer-up flowscoil, ultimately into the coil increasing in the samethe sensor direction sensit andivity maximizes, as shown in the Figure mutual in the5b. plane of the bottom layer flows into the coil in the same direction and maximizes the mutual inductance value of the pick-up coil, ultimately increasing the sensor sensitivity, as shown in Figure5b. inductanceFigure value 6a ofshows the pick the- updirection coil, ultimately of current increasing and Figure the 6 sensorb,c illustrate sensit ivitythe ,distribution as shown in of Figure the Figure6a shows the direction of current and Figure6b,c illustrate the distribution of the magnetic 5b. magnetic field between the sensor and the conductor when a 5 A conductor current flows in the field between the sensor and the conductor when a 5 A conductor current flows in the proposed proposedFigure 6doublea shows-layer the rectangle direction sensor of current model. Inand the Figure figure, the6b,c arrow illustrate indicates the thedistribution direction ofof the the double-layer rectangle sensor model. In the figure, the arrow indicates the direction of the current, magneticcurrent, field and betweenthe magnetic the sensorfield diagram and the shows conductor the magnetic when a flux5 A densityconductor value current according flows to in the the proposedanddistance the magneticdouble between-layer fieldthe rectanglecoil diagram and the sensor shows conductor model. the magneticon In three the sides.figure, flux density the arrow value indicates according the direction to the distance of the current,between and the the coil magnetic and the conductor field diagram on three shows sides. the magnetic flux density value according to the distance between the coil and the conductor on three sides.

J[A/m2]

2.18×108 1.37×108 8.70×107 5.49×107 J[A/m2] 3.46×107 7 2.18×1082.18×10 7 1.37×1081.37×10 6 8.70×1078.70×10 6 5.49×1075.49×10 6 3.46×1073.46×10 2.18×106 2.18×107 1.37×107 8.70×106 5.49×106 3.46×106 2.18×106 Energies 2020, 13, x FOR PEER REVIEW 7 of 16 (a) (b)

(a) (b)

(c)

FigureFigure 6. 6.PCB PCB circuit circuit analysis analysis using using finite finite element element method: method: ( a()a) current current flow flow of of 5 5×101000 A;A; ((bb)) toptop viewview of × magneticof magnetic flux density;flux density; (c) side (c) side view view of magnetic of magnetic flux flux density. density.

3.2. Single-layer Rectangular Pick-Up Coil Figure 7b shows the geometry of the single coil based on the lump equivalent circuit of a model, as shown in Figure 7a, where a is the distance from the trace through which the primary current flows ℼ to the coil, and w is the width of the coil. Thus, when the magnetic field flux formed by the current passes through area S, the magnetic flux in the area is calculated as follows.

Lc Rc a d a id b w

e(t) = -M·did /dt Cc Rd V Vo a i d

GND Coil (a) (b)

Figure 7. Proposed pick-up coil model: (a) equivalent model; (b) geometry of a single coil.

ℼ φ =∫ B ⋅ ds (5) s When this magnetic flux enters the sensor core, the EMF in the terminal of the sensor coil loop is defined according to Faraday’s law as follows. dφ d di e() t =−=−B ⋅=− ds M ∫ s (6) dt dt s dt In addition, the magnetic flux formed by the current trace on the three sides enters in the same direction and same area in the sensor coil and penetrates the coil. The generated magnetic flux is calculated as shown below:

ad++ab µµµoo⋅I bd⋅I o⋅⋅bI  d µ o⋅⋅dI  b φ =2 ∫∫dt +dt =ln 1 ++ln  1 + (7) 22ππaadb π a2 π  a Thus, the EMF induced by the magnetic flux passing through the coil area is calculated according to Faraday’s law as follows:

µo d d  b di eb(t)=− ln 1 ++ ln  1 + (8) π a 2 a dt From Equations (6) and (8), the mutual inductance of the coil is formulated as:

Energies 2020, 13, x FOR PEER REVIEW 7 of 16

(c)

Figure 6. PCB circuit analysis using finite element method: (a) current flow of 5×100 A; (b) top view Energiesof 2020magnetic, 13, 5161 flux density; (c) side view of magnetic flux density. 7 of 15

3.2. Single-layer Rectangular Pick-Up Coil 3.2. Single-layer Rectangular Pick-Up Coil Figure 7b shows the geometry of the single coil based on the lump equivalent circuit of a ℼ model, Figure7b shows the geometry of the single coil based on the lump equivalent circuit of a model, as shown in Figure 7a, where a is the distance from the trace through which the primary current flows as shown in Figure7a, where a is the distance from the trace through which the primary current flows to the coil, and w is the width of the coil. Thus, when the magnetic field flux formed by the current to the coil, and w is the width of the coil. Thus, when the magnetic field flux formed by the current passes through area S, the magnetic flux in the area is calculated as follows. passes through area S, the magnetic flux in the area is calculated as follows.

Lc Rc a d a id b w

e(t) = -M·did /dt Cc Rd V Vo a i d

Coil GND (a) (b)

Figure 7. Proposed pick-up coil model: ( (aa)) equivalent equivalent ℼ model;model; ( (bb)) geometry geometry of of a a single single coil. coil.

φ =⋅  BdsZ (5) φ =s B ds (5) · When this magnetic flux enters the sensor core,s the EMF in the terminal of the sensor coil loop is definedWhen according this magnetic to Faraday’s flux enters law the as sensorfollows. core, the EMF in the terminal of the sensor coil loop is defined according to Faraday’s law as follows.ddφ di et()=− =− Bds ⋅ =− M (6) dt dt s dt s Z dφ d di In addition, the magnetic eflux(t) =formed by= the currentB ds trace= onM thes three sides enters in the same(6) − dt −dt · − dt direction and same area in the sensor coil and penetratess the coil. The generated magnetic flux is calculated as shown below: In addition, the magnetic flux formed by the current trace on the three sides enters in the same μμμ⋅⋅⋅⋅⋅⋅IIbIdIad++bd ab  d μ  b direction andφ same=+=+++2ln1ln1oo area in thedt sensor coil dtand penetrates o the coil. o The generated magnetic flux(7) is ππaa π π  calculated as shown22 below:db a 2  a

Thus, the EMF inducedZ a+d by the magneticZ a+ fluxb passing through the coil! area is calculated ! according µo I b µo I d µo b I d µo d I b to Faraday’sφ =law2 as ·follows: dt + · dt = · · ln 1 + + · · ln 1 + (7) 2π a d 2π a b π a 2π a μ o dd  bdi eb(t)=− ln 1 + + ln  1 + (8) Thus, the EMF induced by the magneticπ  ﬂux passingaadt2 through  the coil area is calculated according to Faraday’s law as follows: From Equations (6) and (8), the mutual inductance of the coil is formulated as: ( ! !) µo d d b di e(t) = b ln 1 + + ln 1 + (8) − π a 2 a dt

From Equations (6) and (8), the mutual inductance of the coil is formulated as: ( ! !) µo d d b Ms = b ln 1 + + ln 1 + . (9) π a 2 a

When the current of frequency f ﬂows in a conductor, the skin depth at the conductor surface is calculated as follows, where γ represents the conductivity of the conductor:

1 δ = p (10) π f µoγ Energies 2020, 13, x FOR PEER REVIEW 8 of 16

μ dd  b =+++o . Mbs ln 1 ln  1 (9) π aa2  When the current of frequency f flows in a conductor, the skin depth at the conductor surface is calculated as follows, where γ represents the conductivity of the conductor: δ = 1 Energies 2020, 13, 5161 πμγ 8 of(10) 15 f o

3.3.3.3. Multilayer Rectangular Pick-Up CoilCoil TheThe proposed model is composed of of two two single single coils coils in in series, series, as as shown shown in in Figure Figure 8.8 .The The coils coils of ofeach each layer layer have have a self-inductance a self-inductance value value of Ln, ofandL neach, and coil each forms coil a formsmutual a inductance mutual inductance with the other. with theHere, other. m12 Here,representsm12 represents the mutual the inductance mutual inductance value be valuetween between the firstthe layer ﬁrst and layer the and second the second layer. layer.Moreover, Moreover, the direction the direction of the ofcoil the current coil current of each of layer each is layer connected is connected in series, in series,as illustrated as illustrated in Figure in Figure5a; therefore,5a; therefore, the inductance the inductance of the of entire the entire coil is coil a value is a value obtained obtained by adding by adding the self-inductance the self-inductance and andmutual mutual inductance inductance components components in each in layer. each layer.As a parameter As a parameter for the dynamic for the dynamic performance performance analysis analysisof the multi-coil, of the multi-coil, the total theinductance total inductance is calculated is calculated using Equation using Equation (12). (12).

m12 Ltot

FigureFigure 8.8. Geometry of single rectangularrectangular coil.coil.

φ LL I " 11# = "11 12 #" # φ1φ L11 L 12 I1 (11) 22=LL21 22 I (11) φ2 L21 L22 I2 LLLm=++ Ltottot = 11L11 + 22L22 12+ m12 (12)(12) TheThe resistanceresistance ofof thethe multilayermultilayer coilcoil isis asas shownshown below:below: RR= 2 tot s (13) Rtot = 2Rs (13) The mutual inductance m12 between single coils is calculated as follows [16] and [17]. Here, d denotesThe the mutual distance inductance betweenm 12thebetween single coils, single l denotes coils iscalculated the length as of follows a single [16 coil] and loop. [17 Here,]. Here, it isd denotesassumed the that distance the self-inductance between the of single the two coils, coilsl denotes is as shown the lengthbelow: of a single coil loop. Here, it is assumed that the self-inductance of the two coils is as shown below: 22 μ l ll  ll m =++−++o ln 1s 1 s  12 π    !2  !2  (14) 2µol ddl l   ddl l  m = ln + 1 +  1 + +  (14) 12     2π  d d  − d d M = 2M multi s (15) Mmulti = 2Ms (15)

3.4.3.4. Parameter Selection for Sensor DesignDesign TheThe transfertransfer functionfunction ofof thethe pick-uppick-up coilcoil basedbased inin thethe lumpedlumped modelmodel atat thethe initialinitial conditioncondition isis asas shownshown below:below: Vs() ⋅⋅ ==o Ms = Ms Gscoil () V (s) M s M s ( ) = Is()o = LRRCRR++LCss=()()−− ss Gcoil s d 2 ++ccdccd+· + cc 12· (16)(16) ( ) ()LCcc s s (2 Lc RcR )dCc Rc Rd ( )( ) Id s (LcCc)s + s( ) + LcCc s s1 s s2 RRddRd Rd − −

Here, the optimal damping resistance Rd is calculated using Equation (18), based on the damping ratio ζ [32]. ! r 1 Lc Rd ς = + RcCc (17) 2 √LcCc Rd Rd + Rc

Lc Rd = q (18) 2 2 2LcCc R C − c c Energies 2020, 13, x FOR PEER REVIEW 9 of 16

Here, the optimal damping resistance Rd is calculated using Equation (18), based on the damping ratio ζ [32]. LR ς =+1 cd RCcc (17) RRR+ 2 LCccddc Energies 2020, 13, 5161 9 of 15 L = c Rd (18) 2LC− RC22 Further, the resonance frequency is calculatedcc as follows: c c Further, the resonance frequency is calculated as follows: 1 f = 1 (19) f res= res π 2π √LcCc (19) 2 LCcc Two poles for coil design are formulatedformulated as presentedpresented below:below: 111 RRR+++ R LRRC1 L + R R C ff=== cdc d, = ccdcc c d c f112ππ+ , f2 (20)(20) 222πLRRCccdcLc + RcRdCc 2 RRLπ cdcRcRdLc

InIn the casecase of of an an integrator integrator design, design, an activean active inverting inverting integrator integrator is applied is applied [32–35], [32–35], and a integrator and a integrator resistor Rf and integrator capacitor Cf are added to the operational amplifier (OP-Amp) to resistor Rf and integrator capacitor Cf are added to the operational amplifier (OP-Amp) to limit limitthe integrator the integrator infinite infinite gain gain value value to a to finite a finite gain gain value value when when a current a current of low of low frequency frequency and and the the DC DCcomponent component flows flows in the in integratorthe integrator in Figure in Figure9. 9.

Cf iint R1 Vout V1= 0 Vin

Figure 9. OptimizedOptimized integral integral circuit. circuit.

Moreover, the integrator current iiintint isis calculated calculated using using the the following following equation: equation: VV−− V V ==V111 Vinin out Vout ()V1 = iVint 1 0 (21) iint = R− =RC − (V1 = 0) (21) Ri1 fiR C i1 f k i Further, the input/output gain value is calculated according to the following equation: Further, the input/output gain value is calculated according to the following equation: × 1 R f " # RjCω 1 f × jωC R C R +1 1 " R # " # Vo f R + f jωC f 1 (22) = k =f ω = τ = R f C (22) V RCffjC R 1 Vin o =−− R1 =−− R1 = −− R ⋅1 · 1 + jωR f C()τ =RC ⋅ · VR R R1+ jRCω f in 111f where R1 is the reverse terminal resistance. whereFrom R1 is the the frequency reverse terminal response resistance. graph illustrated in Figure 10, it can be observed that when designing From the frequency response graph illustrated in Figure 10, it can be observed that when the integrator, the unit gain frequency fr is the value obtained by multiplying the cutoﬀ frequency fc designingand the gain the at integrator, the corner the frequency unit gain using frequency Equation fr is (24) the according value obtained to the gain by multiplying bandwidth product.the cutoff frequency fc and the gain at the corner frequency using Equation (24) according to the gain bandwidth product. ωc 1 fc = = (23) 2π 2πR f C f

R f 1 fr = gain f fc fc = fc = (24) → · R1 · 2πR1C f

The non-inverting terminal resistance R2 located in the OP-Amp terminal constitutes the integrator, inverted and noninverted terminal resistors to minimize bias current error and is set to the same value (25). R1 R f R2 = R1 R f = · (25) k R1 + R f Energies 2020, 13, 5161 10 of 15 Energies 2020, 13, x FOR PEER REVIEW 10 of 16

1 1 f = f = f = 654MHz c 2π R C r 2π R C res ff 1 f Figure 10. FrequencyFrequency response characteristics of the current sensor.

Figure 10 shows the frequency responseω of the coil, integrator, and all the sensors. Sufficient sensor ==c 1 bandwidth must be secured for accuratefc transient response analysis when measuring the current for 22ππRC (23) high-speed GaN power semiconductors. Thus, it is necessaryff to set the appropriate parameter values for the integrator and pick-up coil and to correspondinglyR adjust the pole values in the magnitude-frequency =⋅=⋅=f 1 response of the sensor. fgainfrffcc→ f (24) c RRC2π 110.35 f BW = (26) The non-inverting terminal resistance R2 locatedtrise in the OP-Amp terminal constitutes the integrator,The GaN inverted device and used noninverted in this study terminal was GS66508T,resistors to which minimize is manufactured bias current error by GaN and Systems;is set to moreover,the same value the device (25). resonant frequency fres that was calculated based on Equation (19) at a current increase time of 1.5 ns was determined to be 220 MHz.⋅ RR1 f Accordingly, the sensor bandwidthRRR for== ensuring accurate measurement results must be secured(25) to 21f RR+ a value that is at least two to three times the value of1 thef bandwidth of the power semiconductor [31]. Therefore,Figure when 10 shows the integrator the frequency cutoff responsefrequency of isthe set co toil,1 integrator, kHz, it is possibleand all the to guaranteesensors. Sufficient a sensor bandwidthsensor bandwidth of over must 440 MHz. be secured Further, for the accurate transfer transient function ofresponse the current analysis sensor when with measuring the integrated the sensorcurrent coil for andhigh-speed integrator GaN is obtained power assemiconductors. follows. Thus, it is necessary to set the appropriate parameter values for the integrator and pick-up coil and to correspondingly adjust the pole values in Vsen(s) R f 1 M s Gsen(s) = GINT(s) G (s) = = + · + (27) the magnitude-frequency responsecoil of the sensor.Is(s) R1 1+R f Cs 2 Lc RcRdCc Rc Rd · − × (LcCc)s +s( )+ · Rd Rd 0.35 BW = Moreover, the measurement sensitivity is obtained as shown below: (26) trise The GaN device used in this study was GS66508T,R which is manufacturedV by GaN Systems; K = G = d M (28) sen sen s =resjωc moreover, the device resonant frequency| | f that wasR1C calculatedf (Rc + Rd) based· A on Equation (19) at a current increase time of 1.5 ns was determined to be 220 MHz. InAccordingly, this case, assuming the sensorR bandwidthRc, the sensorfor ensuring measurement accurate sensitivity measurement can beresults calculated must be as follows:secured d to a value that is at least two to three times the value of the bandwidth of the power semiconductor 1 V [31]. Therefore, when the integratorK sencutoff frequencyM = is 2setπ f rto M1 kHz, it is possible to guarantee a sensor(29) ≈ R C · · A bandwidth of over 440 MHz. Further, the transfer1 f function of the current sensor with the integrated sensorIn coil Equation and integrator (29), the sensitivityis obtained of as the follows. sensor is expressed as a product of the unit gain frequency  value of the integrator and theVs mutual()  inductanceR f 1 value between the traceMs⋅ through which the primary GsG()=⋅==− () sGs () sen  × sen INT coil Is() R 1+⋅ R Cs LRRCRR++ current flows and the pick-up coil.sf Thus, the1 sensitivity and bandwidth2 ++ ofccdccd the sensor are simultaneously(27) ()LCcc s s ( ) RRdd Moreover, the measurement sensitivity is obtained as shown below:

Energies 2020, 13, x FOR PEER REVIEW 11 of 16

R KG==d ⋅ MV sen sen sj= ω (28) c ()+ A RC1 fc R R d

In this case, assuming Rd ≫ Rc, the sensor measurement sensitivity can be calculated as follows: 1 KMfM≈⋅=⋅2π V sen r A (29) RC1 f In Equation (29), the sensitivity of the sensor is expressed as a product of the unit gain frequency value of the integrator and the mutual inductance value between the trace through which the primary current flows and the pick-up coil. Thus, the sensitivity and bandwidth of the sensor are simultaneously affected by the parameter values of the coil inductance and integrator; consequently, careful parameter selection is required when designing the sensor.

4. Experimental Verification

Figure 11 a,b shows the shunt resistor sensor and the daughter board prototype of the double pulse test circuit. In the case of the switch current, the integrator output of the pick-up coil was compared with the results of the shunt resistor, and the load current was measured using a current sensor (LeCroy) with a maximum current of 310 A and 0.1 V/A output gain ratio. The prototype has two switches and a double-layer pick-up coil to measure the lower switch current in the half-bridge structure. The main and daughter boards are connected vertically through a connector head; Figure Energies11c shows2020, 13the, 5161 overall double pulse test set including an active integrator, digital signal processor11 of 15 board, inductor, main board, and daughter board. Table 2 lists the parameter values of the proposed coil and integrator. aﬀected by the parameter values of the coil inductance and integrator; consequently, careful parameter selection is required when designingTable 2. the Circuit sensor. parameters of current sensor.

4. Experimental Veriﬁcation Parameter Values (Unit) Mutual Inductance 3.49 nH Figure 11a,b shows the shunt resistor sensor and the daughter board prototype of the double Self-Inductance 21.32 nH pulse test circuit. In the case of the switch current, the integrator output of the pick-up coil was Self-Capacitance 0.7 pF compared with the results of the shunt resistor, and the load current was measured using a current Self-Resistance 0.034 Ω sensor (LeCroy) with a maximum current of 310 A and 0.1 V/A output gain ratio. The prototype has Damping Resistance 120 Ω two switches and a double-layer pick-up coil to measure the lower switch current in the half-bridge Integrator Resistance 72 Ω structure. The main and daughter boards are connected vertically through a connector head; Figure 11c Integrator Capacitance 470 pF shows the overall double pulse test set including an active integrator, digital signal processor board, inductor, main board, and daughter board. Table2 lists the parameter values of the proposed coil and integrator.

Daughter board

upper switch DC cap. Gate region

Current lower switch shunt DC cap.

Pick-up coil

Energies 2020, 13, x FOR PEER REVIEW 12 of 16 (a) (b)

main board

daughter board DSP board

integrator

inductor

(c)

Figure 11. Prototype board of double pulse test: ( a)) current shunt; ( b) daughter board with pick-up coil; ( c) overall double pulse test board.

Figure 12 shows the output waveform of the current shunt and pick-up coil before and after the switching operation. In Figure 12b, during the switch-off operation, the positive peak output value is +5.4 V. Conversely, during the switch-on operation, the positive peak output value is +1.94 V.

Load current Current shunt

0 Current (A)

Time (2μ s/div) (a)

10 10 8 8 6 6 4 4 2 2 1.94V 0 0 Voltage (V) Voltage (V) -2 -2 -4 -4 -6 -6 Time (100ns/div) Time (100ns/div) (b) (c)

Energies 2020, 13, x FOR PEER REVIEW 12 of 16

main board

daughter board DSP board

Energies 2020, 13, 5161 12 of 15

Table 2. Circuit parameters of current sensor. integrator Parameter Values (Unit) inductor Mutual Inductance 3.49 nH Self-Inductance 21.32 nH Self-Capacitance 0.7 pF Self-Resistance(c) 0.034 Ω Damping Resistance 120 Ω Figure 11. Prototype board of doubleIntegrator pulse Resistance test: (a) current shunt; 72 Ω (b) daughter board with pick-up coil; (c) overall double pulse testIntegrator board. Capacitance 470 pF

Figure 12 shows the output waveform of the current shunt and pick-up coil before and after the Figure 12 shows the output waveform of the current shunt and pick-up coil before and after switching operation. In Figure 12b, during the switch-off operation, the positive peak output value is the switching operation. In Figure 12b, during the switch-oﬀ operation, the positive peak output value +5.4 V. Conversely, during the switch-on operation, the positive peak output value is +1.94 V. is +5.4 V. Conversely, during the switch-on operation, the positive peak output value is +1.94 V.

Load current Current shunt

0 Current (A)

Time (2μ s/div) (a)

10 10 8 8 6 6 4 4 2 2 1.94V 0 0 Voltage (V) Voltage (V) -2 -2 -4 -4 -6 -6 Time (100ns/div) Time (100ns/div) (b) (c)

Figure 12. Measured current shunt results and coil output without the integrator following switch behavior: (a) current shunt; (b) output of pick-up coil during switch-oﬀ condition; (c) output of pick-up coil during switch-on condition.

Figure 13 compares the integrator output value of the proposed coil with the sensor result of the 100 mΩ coaxial shunt resistor, manufactured by T&M Research Products, to compare the transient state of the switch current when the switching operation changes in a DC voltage environment of 100 V. In the switch-off stage, the result of the pick-up coil shows a peak value of approximately 1.6 V when compared to the result of the shunt resistor. This is the influence of the high dv/dt of the wide bandgap device; further, the influence of other factors such as the coupling capacitance between the coil and the conductor is reflected. In the switch-on section, the waveform in the switching operation is at a similar level as the waveforms in the two sensors. Energies 2020, 13, x FOR PEER REVIEW 13 of 16

EnergiesFigure 2020, 1312., x Measured FOR PEER REVIEWcurrent shunt results and coil output without the integrator following switch13 of 16 behavior: (a) current shunt; (b) output of pick-up coil during switch-off condition; (c) output of pick- Figureup coil 12.during Measured switch-on current condition. shunt results and coil output without the integrator following switch behavior: (a) current shunt; (b) output of pick-up coil during switch-off condition; (c) output of pick- upFigure coil during13 compares switch-on the condition. integrator output value of the proposed coil with the sensor result of the 100 mΩ coaxial shunt resistor, manufactured by T&M Research Products, to compare the transient state Figureof the switch13 compares current the when integrator the switching output valueoperation of the changes proposed in a coil DC withvoltage the environmentsensor result of 100the 100V. In m theΩ coaxial switch-off shunt stage, resistor, the result manufactured of the pick-up by T&M coil Research shows a Products,peak value to of compare approximately the transient 1.6 V statewhen of compared the switch to current the result when of the shuntswitching resistor. oper Thationis is changes the influence in a DC of voltage the high environment dv/dt of the of wide 100 V.bandgap In the device;switch-off further, stage, the the influe resultnce of ofthe other pick-up factors coil such shows as thea peak coupling value capacitance of approximately between 1.6 the V whencoil and compared the conductor to the isresult reflected. of the In shunt the switch-o resistor.n Th section,is is the the influence waveform of thein the high switching dv/dt of operation the wide bandgapis at a similar device; level further, as the thewaveforms influence in of the other two factors sensors. such as the coupling capacitance between the coil and the conductor is reflected. In the switch-on section, the waveform in the switching operation isEnergies at a similar2020, 13 ,level 5161 as the waveforms in the two sensors. 13 of 15

2 2

21 21

10 10 Current (A) Current Current (A)

-10 -10 Current (A) Current Current (A) -1 Time (100ns/div) -1 Time (100ns/div) (a) (b) Time (100ns/div) Time (100ns/div) Figure 13. Measured (pick-upa) coil sensor output following switch behavior when(b) the DC link voltage is 100 V: (a) switch turn-off; (b) switch turn-on. FigureFigure 13. 13. MeasuredMeasured pick-up pick-up coil sensor output followingfollowing switchswitch behaviorbehavior when when the the DC DC link link voltage voltage is isFigure100 100 V: V: ( a14 )(a switch ) presentsswitch turn-o turn-off; theff;( resultsb )(b switch) switch fo turn-on.r aturn-on. DC voltage environment of 250 V. Overall, the integrator output value of the pick-up coil in the transient response section shows a waveform similar to that of Figure 14 presents the results for a DC voltage environment of 250 V. Overall, the integrator output the shuntFigure resistor 14 presents sensor the when results compared for a DC to the voltage case ofenvironment a DC link voltage of 250 ofV. 100 Overall, V. And the the integrator result in value of the pick-up coil in the transient response section shows a waveform similar to that of the shunt outputthe switch-on value of section the pick-up is more coil accurate in the transientthan that reinsponse the switch-off section showssection. a However,waveform the similar occurrence to that of resistor sensor when compared to the case of a DC link voltage of 100 V. And the result in the switch-on thea positive shunt resistorpeak value sensor in the when switch-off compared section to the indicates case of thea DC same link result voltage as inof the100 caseV. And of the the 100 result V DC in section is more accurate than that in the switch-off section. However, the occurrence of a positive peak thelink switch-on voltage. section is more accurate than that in the switch-off section. However, the occurrence of avalue positive in the peak switch-o value ffinsection the switch-off indicates section the same indicates result the as insame the caseresult of as the in 100the Vcase DC of link the voltage.100 V DC link voltage.

2 2

21 21

1 0 10 Current (A) Current Current (A) Current

-10 -10 Current (A) Current Current (A) Current

-1 -1 Time (100ns/div) Time (100ns/div) (a) (b) Time (100ns/div) Time (100ns/div) FigureFigure 14. 14. MeasuredMeasured pick-up(a pick-up) coil coil sensor sensor output output following following switch switch behavior behavior(b for) for a DC a DC link link voltage voltage of 250of 250 V: ( V:a) (switcha) switch turn-off; turn-o (ffb;() bswitch) switch turn-on. turn-on. Figure 14. Measured pick-up coil sensor output following switch behavior for a DC link voltage of 5.5. Conclusions Conclusions250 V: (a) switch turn-off; (b) switch turn-on. In this study, a pick-up coil, which is a current sensor for measuring the switch current of 5. ConclusionsIn this study, a pick-up coil, which is a current sensor for measuring the switch current of a half- bridgea half-bridge based on based a non-modular on a non-modular GaN power GaN powersemiconductor, semiconductor, was proposed. was proposed. The proposed The proposed coil sensor coil measuressensorIn this measures the study, lowerthe a pick-up lowerswitch switchcoil, current which current at is thea atcurrent thebottom bottom sensor of ofthe for the measuringhalf-bridge; half-bridge; the moreover, moreover,switch current the the structural of a half- bridgecharacteristic based on includes a non-modular a trace wrapped GaN power around semiconductor, a rectangular sensor was proposed. coil composed The proposed of a 4.2 mm coil 3.4sensor mm × measuresdouble layer the on lower three switch sides through current which at the the bottom primary of currentthe half-bridge; to be measured moreover, flows. the This structural structure aims to secure the maximum bandwidth and achieve high measurement sensitivity for the GaN device with fast switching characteristics. This was confirmed through inductance comparison analysis with the conventional coil structure using the finite element method as well as frequency response analysis through mathematical modeling based on parameter values. Moreover, experimental verification was conducted using the double pulse test through an analysis process for the transient situation for switch-on and switch-off conditions in a DC voltage environment ranging from 100 to 250 V. However, this paper did not consider the issue of the coupling capacitance noise between the coil and the conductor, and accordingly, some overshoot components were seen in the switch-off condition, which appeared in the experimental results. In the future, further studies on reinforcement of this issue and discussion on solutions are needed. Energies 2020, 13, 5161 14 of 15

Author Contributions: Conceptualization, U.-J.K. and R.-Y.K.; methodology, U.-J.K.; software, M.-S.S., U.-J.K.; validation, U.-J.K.; formal analysis, U.-J.K. and M.-S.S.; investigation, U.-J.K.; resources, U.-J.K.; data curation, U.-J.K.; writing—original draft preparation, U.-J.K.; writing—review and editing, U.-J.K. and R.-Y.K.; visualization, U.-J.K.; supervision, U.-J.K.; project administration, R.-Y.K.; funding acquisition, R.-Y.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Korea Institute of Energy Technology Evaluation and Planning grant number 2018201010650A, 20184010201710. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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